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E-raamat: Wave Theory of Information

(University of California, San Diego)
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  • Ilmumisaeg: 30-Nov-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108546812
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  • Formaat: EPUB+DRM
  • Ilmumisaeg: 30-Nov-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108546812
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Understand the relationship between information theory and the physics of wave propagation with this expert guide. Balancing fundamental theory with engineering applications, it describes the mechanism and limits for the representation and communication of information using electromagnetic waves. Information-theoretic laws relating functional approximation and quantum uncertainty principles to entropy, capacity, mutual information, rate distortion, and degrees of freedom of band-limited radiation are derived and explained. Both stochastic and deterministic approaches are explored, and applications for sensing and signal reconstruction, wireless communication, and networks of multiple transmitters and receivers are reviewed. With end-of-chapter exercises and suggestions for further reading enabling in-depth understanding of key concepts, it is the ideal resource for researchers and graduate students in electrical engineering, physics and applied mathematics looking for a fresh perspective on classical information theory.

An expert guide to the relationship between information theory and the physics of wave propagation, covering stochastic and deterministic approaches, engineering applications, and the universal physical limits of radiation. It is an ideal reference for researchers and graduate students in electrical engineering, physics, and applied mathematics.

Arvustused

'This is an excellent textbook that ties together information theory and wave theory in a very insightful and understandable way. It is of great value and highly recommended for students, researchers and practitioners. Professor Franceschetti brings a highly valuable textbook based on many years of teaching and research.' Charles Elachi, California Institute of Technology and Director Emeritus of the Jet Propulsion Laboratory at NASA 'This book is about the physics of information and communication. It could be considered to be an exposition of Shannon information theory, where information is transmitted via electromagnetic waves. Surely Shannon would approve of it.' Sanjoy K. Mitter, Massachusetts Institute of Technology 'Communication and information are inherently physical. Most of the literature, however, abstracts out the physics, treating them as mathematical or engineering disciplines. Although abstractions are necessary in the design of systems, much is lost in understanding the fundamental limits and how these disciplines fit together with the underlying physics. Franceschetti breaks the disciplinary boundaries, presenting communication and information as physical phenomena in a coherent, mathematically sophisticated, and lucid manner.' Abbas El Gamal, Stanford University, California 'This is an ambitious and important book exceedingly well written, and surprisingly thin, given the amount of material. The mathematics, supplemented by considerable intuitive explanation, is never overwhelming, and should be readily followed by the diligent reader. There are extensive references, and a useful summary at the end of each chapter, along with well-crafted exercises. Unquestionably this book will contribute hugely to [ Professor] Franceschetti's goal: 'to break through the compartmentalized walls of several disciplines' any researcher who purports to work on the advancement of wireless communication theory should take time to study Wave Theory of Information.' Thomas L. Marzetta, IEEE Information Theory Society Newsletter 'Compared to other books, Wave Theory of Information takes a different approach to information theory. It does so by presenting the relationship between information theory and the physics of wave propagation, using electromagnetic waves to describe the representation and communication of information a textbook for a graduate course in communication and information theory, [ it] is intended for PhD students and researchers in electrical engineering.' Edward S. Krebes, The Leading Edge

Muu info

Understand the relationship between information theory and the physics of electromagnetic wave propagation with this expert guide.
Preface xvii
Notation xx
1 Introduction
1(47)
1.1 The Physics of Information
1(4)
1.1.1 Shannon's Laws
1(1)
1.1.2 Concentration Behaviors
2(2)
1.1.3 Applications
4(1)
1.2 The Dimensionality of the Space
5(8)
1.2.1 Bandlimitation Filtering
5(2)
1.2.2 The Number of Degrees of Freedom
7(2)
1.2.3 Space--Time Fields
9(2)
1.2.4 Super-resolution
11(2)
1.3 Deterministic Information Measures
13(5)
1.3.1 Kolmogorov Entropy
14(1)
1.3.2 Kolmogorov Capacity
14(3)
1.3.3 Quantized Unit of Information
17(1)
1.4 Probabilistic Information Measures
18(15)
1.4.1 Statistical Entropy
19(2)
1.4.2 Differential Entropy
21(1)
1.4.3 Typical Waveforms
22(1)
1.4.4 Quantized Typical Waveforms
23(2)
1.4.5 Mutual Information
25(1)
1.4.6 Shannon Capacity
26(3)
1.4.7 Gaussian Noise
29(1)
1.4.8 Capacity with Gaussian Noise
30(3)
1.5 Energy Limits
33(8)
1.5.1 The Low-Energy Regime
33(1)
1.5.2 The High-Energy Regime
34(1)
1.5.3 Quantized Radiation
35(2)
1.5.4 Universal Limits
37(4)
1.6 Tour d'Horizon
41(2)
1.7 Summary and Further Reading
43(1)
1.8 Test Your Understanding
44(4)
2 Signals
48(39)
2.1 Representations
48(1)
2.2 Information Content
49(6)
2.2.1 Bandlimited Signals
50(1)
2.2.2 Timelimited Signals
51(1)
2.2.3 Impossibility of Time-Frequency Limiting
52(1)
2.2.4 Shannon's Program
53(2)
2.3 Heisenberg's Uncertainty Principle
55(5)
2.3.1 The Uncertainty Principle for Signals
55(1)
2.3.2 The Uncertainty Principle in Quantum Mechanics
56(2)
2.3.3 Entropic Uncertainty Principle
58(1)
2.3.4 Uncertainty Principle Over Arbitrary Measurable Sets
58(1)
2.3.5 Converse to the Uncertainty Principle
59(1)
2.4 The Folk Theorem
60(3)
2.4.1 Problems with the Folk Theorem
61(2)
2.5 Slepian's Concentration Problem
63(7)
2.5.1 A "Lucky Accident"
65(1)
2.5.2 Most Concentrated Functions
66(2)
2.5.3 Geometric View of Concentration
68(2)
2.6 Spheroidal Wave Functions
70(5)
2.6.1 The Wave Equation
71(1)
2.6.2 The Helmholtz Equation
72(3)
2.7 Series Representations
75(6)
2.7.1 Prolate Spheroidal Orthogonal Representation
76(2)
2.7.2 Other Orthogonal Representations
78(1)
2.7.3 Minimum Energy Error
79(2)
2.8 Summary and Further Reading
81(2)
2.9 Test Your Understanding
83(4)
3 Functional Approximation
87(43)
3.1 Signals and Functional Spaces
87(1)
3.2 Kolmogorov N-Width
88(2)
3.3 Degrees of Freedom of Bandlimited Signals
90(5)
3.3.1 Computation of the N-Widths
91(4)
3.4 Hilbert--Schmidt Integral Operators
95(9)
3.4.1 Timelimiting and Bandlimiting Operators
98(2)
3.4.2 Hilbert--Schmidt Decomposition
100(2)
3.4.3 Singular Value Decomposition
102(2)
3.5 Extensions
104(9)
3.5.1 Approximately Bandlimited Signals
104(1)
3.5.2 Multi-band Signals
105(3)
3.5.3 Signals of Multiple Variables
108(3)
3.5.4 Hybrid Scaling Regimes
111(2)
3.6 Blind Sensing
113(5)
3.6.1 Robustness of Blind Sensing
115(1)
3.6.2 Fractal Dimension
116(2)
3.7 Compressed Sensing
118(5)
3.7.1 Robustness of Compressed Sensing
119(2)
3.7.2 Probabilistic Reconstruction
121(1)
3.7.3 Information Dimension
122(1)
3.8 Summary and Further Reading
123(1)
3.9 Test Your Understanding
124(6)
4 Electromagnetic Propagation
130(27)
4.1 Maxwell's Equations
130(2)
4.2 Propagation Media
132(6)
4.2.1 Perfectly Conductive Media
134(3)
4.2.2 Dielectric Media
137(1)
4.3 Conservation of Power
138(1)
4.4 Plane Wave Propagation
139(5)
4.4.1 Lossless Case
140(1)
4.4.2 Lossy Case
141(1)
4.4.3 Boundary Effects
142(1)
4.4.4 Evanescent Waves
143(1)
4.5 The Wave Equation for the Potentials
144(2)
4.6 Radiation
146(6)
4.6.1 The Far-Field Region
149(2)
4.6.2 The Fraunhofer Region
151(1)
4.7 Equivalence and Uniqueness
152(1)
4.8 Summary and Further Reading
153(1)
4.9 Test Your Understanding
154(3)
5 Deterministic Representations
157(16)
5.1 The Spectral Domains
157(2)
5.1.1 Four Field Representations
157(1)
5.1.2 The Space--Frequency Spectral Domain
158(1)
5.2 System Representations
159(5)
5.2.1 Linear, Time-Invariant Systems
159(1)
5.2.2 Linear, Time-Invariant, Homogeneous Media
160(1)
5.2.3 Green's Function in Free Space for the Potential
160(1)
5.2.4 Green's Function in Free Space for the Field
161(1)
5.2.5 Green's Function for Cylindrical Propagation
162(2)
5.3 Discrete Radiating Elements
164(3)
5.3.1 Single Transmitter--Receiver Pair
164(2)
5.3.2 Multiple Transmitters and Receivers
166(1)
5.3.3 Singular Value Decomposition
166(1)
5.4 Communication Systems: Arbitrary Radiating Elements
167(4)
5.4.1 Hilbert--Schmidt Decomposition
168(2)
5.4.2 Optimal Communication Architecture
170(1)
5.5 Summary and Further Reading
171(1)
5.6 Test Your Understanding
172(1)
6 Stochastic Representations
173(27)
6.1 Stochastic Models
173(1)
6.2 Green's Function for a Random Environment
174(2)
6.2.1 Linear, Time-Varying Systems
174(2)
6.2.2 Linear, Space-Time-Varying Systems
176(1)
6.3 Multi-path
176(10)
6.3.1 Frequency-Varying Green's Function: Coherence Bandwidth
179(2)
6.3.2 Time-Varying Green's Function: Coherence Time
181(2)
6.3.3 Mutual Coherence Function
183(3)
6.3.4 Spatially Varying Green's Function: Coherence Distance
186(1)
6.4 Karhunen--Loeve Representation
186(10)
6.4.1 Time-Varying Green's Function
187(3)
6.4.2 Optimality of the Karhunen--Loeve Representation
190(1)
6.4.3 Stochastic Diversity
191(2)
6.4.4 Constant Power Spectral Density
193(1)
6.4.5 Frequency-Varying Green's Function
194(1)
6.4.6 Spatially Varying Green's Function
195(1)
6.5 Summary and Further Reading
196(1)
6.6 Test Your Understanding
197(3)
7 Communication Technologies
200(30)
7.1 Applications
200(1)
7.2 Propagation Effects
200(5)
7.2.1 Multiplexing
203(1)
7.2.2 Diversity
204(1)
7.3 Overview of Current Technologies
205(3)
7.3.1 OFDM
205(1)
7.3.2 MC-CDMA
205(1)
7.3.3 GSM
206(1)
7.3.4 DS-CDMA
206(1)
7.3.5 MIMO
207(1)
7.4 Principles of Operation
208(11)
7.4.1 Orthogonal Spectrum Division
209(3)
7.4.2 Orthogonal Code Division
212(4)
7.4.3 Exploiting Diversity
216(1)
7.4.4 Orthogonal Spatial Division
217(2)
7.5 Network Strategies
219(7)
7.5.1 Multi-hop
219(2)
7.5.2 Hierarchical Cooperation
221(1)
7.5.3 Interference Alignment
222(2)
7.5.4 A Layered View
224(1)
7.5.5 Degrees of Freedom
225(1)
7.6 Summary and Further Reading
226(1)
7.7 Test Your Understanding
227(3)
8 The Space--Wavenumber Domain
230(35)
8.1 Spatial Configurations
230(1)
8.2 Radiation Model
231(1)
8.3 The Field's Functional Space
232(1)
8.4 Spatial Bandwidth
233(11)
8.4.1 Bandlimitation Error
234(2)
8.4.2 Phase Transition of the Bandlimitation Error
236(2)
8.4.3 Asymptotic Evaluation
238(2)
8.4.4 Critical Bandwidth
240(3)
8.4.5 Size of the Transition Window
243(1)
8.5 Degrees of Freedom
244(6)
8.5.1 Hilbert--Schmidt Decomposition
246(2)
8.5.2 Sampling
248(2)
8.6 Cut-Set Integrals
250(8)
8.6.1 Linear Cut-Set Integral
251(2)
8.6.2 Surface Cut-Set Integral
253(3)
8.6.3 Applications to Canonical Geometries
256(2)
8.7 Backscattering
258(3)
8.8 Summary and Further Reading
261(1)
8.9 Test Your Understanding
261(4)
9 The Time--Frequency Domain
265(10)
9.1 Frequency-Bandlimited Signals
265(1)
9.2 Radiation with Arbitrary Multiple Scattering
266(6)
9.2.1 Two-Dimensional Circular Domains
267(2)
9.2.2 Three-Dimensional Spherical Domains
269(1)
9.2.3 General Rotationally Symmetric Domains
270(2)
9.3 Modulated Signals
272(1)
9.4 Alternative Derivations
273(1)
9.5 Summary and Further Reading
274(1)
9.6 Test Your Understanding
274(1)
10 Multiple Scattering Theory
275(28)
10.1 Radiation with Multiple Scattering
275(3)
10.1.1 The Basic Equation
276(1)
10.1.2 Multi-path Propagation
277(1)
10.2 Multiple Scattering in Random Media
278(6)
10.2.1 Born Approximation
281(1)
10.2.2 Complete Solutions
281(2)
10.2.3 Cross Sections
283(1)
10.3 Random Walk Theory
284(7)
10.3.1 Radiated Power Density
289(1)
10.3.2 Full Power Density
289(1)
10.3.3 Diffusive Regime
290(1)
10.3.4 Transport Theory
290(1)
10.4 Path Loss Measurements
291(1)
10.5 Pulse Propagation in Random Media
292(7)
10.5.1 Expected Space-Time Power Response
292(4)
10.5.2 Random Walk Interpretation
296(1)
10.5.3 Expected Space--Frequency Power Response
297(1)
10.5.4 Correlation Functions
298(1)
10.6 Power Delay Profile Measurements
299(1)
10.7 Summary and Further Reading
300(1)
10.8 Test Your Understanding
301(2)
11 Noise Processes
303(40)
11.1 Measurement Uncertainty
303(4)
11.1.1 Thermal Noise
303(1)
11.1.2 Shot Noise
304(2)
11.1.3 Quantum Noise
306(1)
11.1.4 Radiation Noise
306(1)
11.2 The Black Body
307(7)
11.2.1 Radiation Law, Classical Derivation
307(4)
11.2.2 Thermal Noise, Classical Derivation
311(1)
11.2.3 Quantum Mechanical Correction
312(2)
11.3 Equilibrium Configurations
314(8)
11.3.1 Statistical Entropy
316(1)
11.3.2 Thermodynamic Entropy
317(1)
11.3.3 The Second Law of Thermodynamics
318(1)
11.3.4 Probabilistic Interpretation
319(1)
11.3.5 Asymptotic Equipartition Property
320(1)
11.3.6 Entropy and Noise
321(1)
11.4 Relative Entropy
322(1)
11.5 The Microwave Window
323(2)
11.6 Quantum Complementarity
325(1)
11.7 Entropy of a Black Body
326(3)
11.7.1 Total Energy
326(1)
11.7.2 Thermodynamic Entropy
327(1)
11.7.3 The Planck Length
328(1)
11.7.4 Gravitational Limits
329(1)
11.8 Entropy of Arbitrary Systems
329(2)
11.8.1 The Holographic Bound
330(1)
11.8.2 The Universal Entropy Bound
330(1)
11.9 Entropy of Black Holes
331(2)
11.10 Maximum Entropy Distributions
333(3)
11.11 Summary and Further Reading
336(2)
11.12 Test Your Understanding
338(5)
12 Information-Theoretic Quantities
343(48)
12.1 Communication Using Signals
343(1)
12.2 Shannon Capacity
344(14)
12.2.1 Sphere Packing
347(2)
12.2.2 Random Coding
349(1)
12.2.3 Capacity and Mutual Information
350(2)
12.2.4 Limiting Regimes
352(2)
12.2.5 Quantum Constraints
354(1)
12.2.6 Capacity of the Noiseless Photon Channel
355(1)
12.2.7 Colored Gaussian Noise
356(1)
12.2.8 Minimum Energy Transmission
357(1)
12.3 A More Rigorous Formulation
358(6)
12.3.1 Timelimited Signals
359(1)
12.3.2 Bandlimited Signals
360(2)
12.3.3 Refined Noise Models
362(2)
12.4 Shannon Entropy
364(4)
12.4.1 Rate-Distortion Function
364(2)
12.4.2 Rate-Distortion and Mutual Information
366(2)
12.5 Kolmogorov's Deterministic Quantities
368(3)
12.5.1 e-Coverings, e-Nets, and e-Entropy
369(1)
12.5.2 e-Distinguishable Sets and e-Capacity
370(1)
12.5.3 Relation Between e-Entropy and e-Capacity
370(1)
12.6 Basic Deterministic--Stochastic Model Relations
371(3)
12.6.1 Capacity
371(2)
12.6.2 Rate-Distortion
373(1)
12.7 Information Dimensionality
374(4)
12.7.1 Metric Dimension
374(2)
12.7.2 Functional Dimension and Metric Order
376(1)
12.7.3 Infinite-Dimensional Spaces
377(1)
12.8 Bandlimited Signals
378(6)
12.8.1 Capacity and Packing
378(1)
12.8.2 Entropy and Covering
378(1)
12.8.3 e-Capacity of Bandlimited Signals
379(2)
12.8.4 (e, δ)-Capacity of Bandlimited Signals
381(1)
12.8.5 e-Entropy of Bandlimited Signals
382(1)
12.8.6 Comparison with Stochastic Quantities
383(1)
12.9 Spatially Distributed Systems
384(4)
12.9.1 Capacity with Channel State Information
384(3)
12.9.2 Capacity without Channel State Information
387(1)
12.10 Summary and Further Reading
388(1)
12.11 Test Your Understanding
389(2)
13 Universal Entropy Bounds
391(16)
13.1 Bandlimited Radiation
391(1)
13.2 Deterministic Signals
392(5)
13.2.1 Quantization Error
393(1)
13.2.2 Kolmogorov Entropy Bound
394(2)
13.2.3 Saturating the Bound
396(1)
13.3 Stochastic Signals
397(3)
13.3.1 Shannon Rate--Distortion Bound
398(1)
13.3.2 Shannon Entropy Bound
398(2)
13.4 One-Dimensional Radiation
400(1)
13.5 Applications
401(2)
13.5.1 High-Energy Limits
401(1)
13.5.2 Relation to Current Technologies
402(1)
13.6 On Models and Reality
403(2)
13.7 Summary and Further Reading
405(1)
13.8 Test Your Understanding
406(1)
Appendix A Elements of Functional Analysis 407(15)
Appendix B Vector Calculus 422(6)
Appendix C Methods for Asymptotic Evaluation of Integrals 428(5)
Appendix D Stochastic Integration 433(1)
Appendix E Special Functions 434(3)
Appendix F Electromagnetic Spectrum 437(1)
Bibliography 438(9)
Index 447
Massimo Franceschetti is a Professor in the Department of Electrical and Computer Engineering at the University of California, San Diego, and a Research Affiliate of the California Institute of Telecommunications and Information Technology. He is the co-author of Random Networks for Communication (Cambridge, 2008).